This one's tough. Who can solve it?

Question

an artitst has an oddly shaped piece of canvas that contains exactly 81 square inches. the small square projecting at the top is 1 in on a side. it is attached to a square of 16 sq in which is in turn attached to a larger square of 64 sq in. that artist wants to make a 9x9 square canvas for his painting. how can he divide the canvas into the smallest number of pieces that will fit together to make a perfect square?

Answer 1

First, the words used in the question are too indefinite to choose between the staircase solution and the four strips of 4x1 solution.

It says "divide the canvas into the smallest number of pieces", so the staircase solution divides one square into two pieces, and another square into two pieces, that's four divided pieces. The four strips solution divides one square into four pieces, that's four divided pieces too. Undivided pieces don't count.

But it's still wrong, because the question says that the three starting squares are ATTACHED to each other, and both the solutions are assuming they've been detached first. Depending on whereabouts they're attached to each other, we might be able to save a piece, but we don't know.

Answer 2

Meg, that's still 6 pieces (the 8x8, the four strips of 4x1 and the 1x1).

I got it... Cut a staircase pattern into the 8x8 piece, starting 1 inch below the top left corner: cut 1 inch right, 1 inch down, 1 inch right, 1 inch down, etc.

Then move the top-right part, one inch down and to the right to fit the staircase again. You now have a 7x9 rectangle with a 1x1 square protruding under the bottom right corner. Put the 1x1 square just below that little protruding square, and fill the rest with two halves of the 4x4 square. Total = 5 pieces!

EDIT: That's 4 pieces, now that I've read your problem correctly - the 1x1 square is already attached to the 8x8 so that's one less piece.

Answer 3

Gianlino's right. Five pieces, cut the 4x4 into strips of 4x1 and lay them along two adjacent sides of the 8x8 with the 1x1 stuffed into the corner.

Answer 4

You can do it with 5 pieces.

To Meg W: that's not what I meant: you have 6 pieces!